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JEE Main 2016 questions

38 questions, by subject. Each opens with its options and answer.

Mathematics

  1. The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along the line x = y = z is

    Three Dimensional Geometry · with solution

  2. The integral ∫ dfrac2x^12 + 5x^9(x^5 + x^3 + 1)^3 dx is equal to

    Indefinite Integration · with solution

  3. The area (in sq units) of the region \(x, y): y^2 ≥ 2x and x^2 + y^2 ≤ 4x, x ≥ 0, y ≥ 0\ is

    Definite Integrals and Areas · with solution

  4. lim_n → ∞ ( frac(n+1)(n+2)·s 3nn^2n )^1/n is equal to

    Definite Integrals and Areas · with solution

  5. Two sides of a rhombus are along the lines, x - y + 1 = 0 and 7x - y - 5 = 0. If its diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus?

    Straight Lines and Pair of Lines

  6. The centres of those circles which touch the circle, x^2 + y^2 - 8x - 8y - 4 = 0, externally and also touch the X-axis, lie on

    Circles · with solution

  7. Let a, b and c be three unit vectors such that a × (b × c) = frac√(3)2(b + c). If b is not parallel to c, then the angle between a and b is

    Vector Algebra · with solution

  8. A computer producing factory has only two plants T_1 and T_2. Plant T_1 produces 20% and plant T_2 produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is…

    Probability

  9. If the line, (x-3)/2 = (y+2)/(-1) = (z+4)/3 lies in the plane, lx + my - z = 9, then l^2 + m^2 is equal to

    Three Dimensional Geometry · with solution

  10. Let P be the point on the parabola, y^2 = 8x, which is at a minimum distance from the centre C of the circle, x^2 + (y+6)^2 = 1. Then, the equation of the circle, passing through C and having its centre at P is

    Conic Sections · with solution

  11. A value of θ for which (2 + 3isinθ)/(1 - 2isinθ) is purely imaginary, is

    Complex Numbers and Quadratic Equations · with solution

  12. The value of sum_k=1^13 1/(sin ((π)/4 + ((k-1)π)/6 )sin ((π)/4 + (kπ)/6 )) is equal to

    Trigonometry · with solution

  13. If one of the diameters of the circle, given by the equation, x^2 + y^2 - 4x + 6y - 12 = 0, is a chord of a circle S, whose centre is at (-3, 2), then the radius of S is

    Circles · with solution

  14. If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is

    Permutations and Combinations

  15. If A = beginbmatrix 5a & -b \ 3 & 2 endbmatrix and A adj A = AA^T, then 5a + b is equal to

    Matrices and Determinants · with solution

  16. Let P = beginbmatrix 1 & 0 & 0 \ 4 & 1 & 0 \ 16 & 4 & 1 endbmatrix and I be the identity matrix of order 3. If Q = [q_ij] is a matrix, such that P^50 - Q = I, then dfracq_31 + q_32q_21 equals

    Matrices and Determinants

  17. If the 2nd, 5th and 9th terms of a non-constant AP are in GP, then the common ratio of this GP is

    Sequences and Series

  18. Let b_i > 1 for i = 1, 2, …, 101. Suppose log_e b_1, log_e b_2, …, log_e b_101 are in AP with the common difference log_e 2. Suppose a_1, a_2, …, a_101 are in AP such that a_1 = b_1 and a_51 = b_51. If t = b_1 + b_2 + ……

    Sequences and Series

  19. Let p = lim_x → 0^+ (1 + tan^2 √(x))^1/2x, then log p is equal to

    Limits Continuity and Differentiability · with solution

  20. Consider f(x) = tan^-1 (√((1+sin x)/(1-sin x)) ), x ∈ (0, (π)/2 ). A normal to y = f(x) at x = (π)/6 also passes through the point

    Application of Derivatives

  21. If the sum of the first ten terms of the series (13/5 )^2 + (22/5 )^2 + (31/5 )^2 + 4^2 + (44/5 )^2 + … is 16/5m, then m is equal to

    Sequences and Series

  22. A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30°. After walking for 10 min from…

    Trigonometry · with solution

  23. If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0, is

    Trigonometry · with solution

  24. A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include atmost one…

    Permutations and Combinations

  25. For x ∈ R, f(x) = |log 2 - sin x| and g(x) = f(f(x)), then

    Limits Continuity and Differentiability

  26. Let S = \x ∈ (-π, π): x ≠ 0, ±(π)/2 \. The sum of all distinct solutions of the equation √(3)sec x + csc x + 2(tan x - cot x) = 0 in the set S is equal to

    Trigonometry

  27. A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum,…

    Application of Derivatives · with solution

  28. If a curve y = f(x) passes through the point (1, -1) and satisfies the differential equation, y(1 + xy)dx = x dy, then f (-1/2 ) is equal to

    Differential Equations · with solution

  29. The system of linear equations x + λ y - z = 0; λ x - y - z = 0; x + y - λ z = 0 has a non-trivial solution for

    Matrices and Determinants

  30. The least value of α ∈ R for which 4α x^2 + 1/x ≥ 1, for all x > 0, is

    Application of Derivatives · with solution

  31. Area of the region \(x, y) ∈ R^2 : y ≥ √(|x+3|), 5y ≤ (x+9) ≤ 15\ is equal to

    Definite Integrals and Areas

  32. The sum of all real values of x satisfying the equation (x^2 - 5x + 5)^x^2 + 4x - 60 = 1 is

    Complex Numbers and Quadratic Equations · with solution

  33. If the number of terms in the expansion of (1 - 2/x + 4/(x^2) )^n, x ≠ 0, is 28, then the sum of the coefficients of all the terms in this expansion, is

    Binomial Theorem · with solution

  34. Let -(π)/6 β_1 and α_2 > β_2, then α_1 + β_2 equals

    Complex Numbers and Quadratic Equations

  35. The value of int_-π/2^π/2 (x^2 cos x)/(1 + e^x) dx is equal to

    Definite Integrals and Areas · with solution

  36. Let P be the image of the point (3, 1, 7) with respect to the plane x - y + z = 3. Then, the equation of the plane passing through P and containing the straight line x/1 = y/2 = z/1 is

    Three Dimensional Geometry

Chemistry

  1. A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of h/λ (where, λ is…

    Atomic Structure

  2. P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is 4π r^2 dr. The qualitative sketch of…

    Atomic Structure

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